如何获取YieldCurve包估计的Nelson Siegel系数标准误

Great question! The Nelson.Siegel() function in the YieldCurve package outputs estimated beta parameters (β₀, β₁, β₂) and λ, but it doesn’t directly provide their standard errors. To calculate these, you can fit the Nelson-Siegel model using nonlinear least squares (NLS) directly in R—this gives you access to the full model summary, including standard errors.

Step-by-Step Solution #

First, let’s start with your existing code to get initial parameter estimates (we’ll use these to help the NLS model converge faster):

library("YieldCurve")
library(dplyr) # For the `first()` function
data(FedYieldCurve)

maturity.Fed <- c(3/12, 0.5, 1, 2, 3, 5, 7, 10)
NSParameters <- Nelson.Siegel(rate = first(FedYieldCurve, '10 month'), maturity = maturity.Fed)

Next, define the Nelson-Siegel model as a function—this is what we’ll use in the NLS fit:

# Define the Nelson-Siegel yield curve formula
nelson_siegel <- function(maturity, b0, b1, b2, lambda) {
  b0 + b1 * (1 - exp(-maturity/lambda))/(maturity/lambda) + 
    b2 * ((1 - exp(-maturity/lambda))/(maturity/lambda) - exp(-maturity/lambda))
}

Now, let’s fit the model for a single month (we’ll use the first month of your 10-month sample as an example). We’ll use the parameters from Nelson.Siegel() as starting values for the NLS fit to ensure convergence:

# Extract yields for the first month
first_month_yields <- as.numeric(first(FedYieldCurve, '10 month')[1, ])

# Fit the NLS model
nls_fit <- nls(
  formula = first_month_yields ~ nelson_siegel(maturity.Fed, b0, b1, b2, lambda),
  start = list(
    b0 = NSParameters[1, "beta0"],
    b1 = NSParameters[1, "beta1"],
    b2 = NSParameters[1, "beta2"],
    lambda = NSParameters[1, "lambda"]
  )
)

Finally, view the model summary—this will include standard errors for each parameter:

# Print the full summary (look for the "Std. Error" column)
summary(nls_fit)

What You’ll See #

The summary output will have a Coefficients section that looks like this (example values):

Estimate Std. Error t value Pr(>|t|)    
b0          2.50123    0.04567   54.77 1.28e-08 ***
b1         -0.23456    0.02134  -10.99  0.00012 ***
b2          0.11234    0.01567    7.17  0.00087 ***
lambda      1.89012    0.23456    8.06  0.00054 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

The Std. Error column gives you the standard error for each parameter (e.g., the standard error for β₀ is 0.04567 in this example).

Batch Processing for All 10 Months #

If you want standard errors for every month in your 10-month sample, you can wrap this in a loop or use purrr::map():

# Load purrr for easier iteration
library(purrr)

# Function to get SEs for a single row of yield data
get_ns_se <- function(yield_row, maturity, start_params) {
  fit <- nls(
    as.numeric(yield_row) ~ nelson_siegel(maturity, b0, b1, b2, lambda),
    start = list(
      b0 = start_params["beta0"],
      b1 = start_params["beta1"],
      b2 = start_params["beta2"],
      lambda = start_params["lambda"]
    )
  )
  # Extract standard errors from the summary
  coef(summary(fit))[, "Std. Error"]
}

# Apply the function to each month
all_se <- map2_df(
  .x = split(first(FedYieldCurve, '10 month'), seq(nrow(first(FedYieldCurve, '10 month')))),
  .y = split(NSParameters, seq(nrow(NSParameters))),
  ~ get_ns_se(.x, maturity.Fed, .y)
)

# View the results
all_se

This will give you a data frame where each row is a month, and each column is the standard error for a parameter.

内容的提问来源于stack exchange，提问作者Roy